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## 6.1 Graphing Quadratic Functions

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**6.1 Graphing Quadratic Functions**Parabola Axis of symmetry Vertex**A Quadratic function**Parts of the Quadratic function. CONSTANT TERM**A Quadratic function**The graph of a Quadratic function is called a parabola.**Parabola are Symmetrical**Axis of Symmetry, splits it down the middle**Parabola are Symmetrical**Points reflect across the axis of symmetry**Parabola are Symmetrical**The equation for the axis symmetry is**The y – Intercept of a parabola**If x = 0, then c is the y intercept**The Vertex of the Parabola**The Vertex is a point at the highest or lowest point of the graph of a parabola. The Vertex is on the axis of symmetry, so its x coordinate is found by**Now that you have x of the Vertex how do you find the y**x = 1**How can you tell if the Vertex is the highest or lowest**point. It all depends on “a”. If a > 0, the parabola If a<0, the parabola is opens upward. opens downward**The Maximum or Minimum value is the y value of the vertex**If the vertex is ( -3, 1), of f(x)= x2 + 6x + 10, then the minimum value is 1. Since the parabola is opening upward it is the minimum.**How to graph the parabolaf(x) = 2- 4x + x2**Rewrite the function. f(x) = x2 -4x + 2 Find the y intercept: f(0) = 02 -4(0) + 2 = 2 (0, 2) Find the vertex: a = 1, b= -4**How to graph the parabolaf(x) = 2- 4x + x2**Start a table using number higher and lower then 2, from the vertex. Plot points**How to graph the parabolaf(x) = 2- 4x + x2**Connects the points.**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3 Does the graph open up or down? What are a , b and c?**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3 Does the graph open up or down? Down What are a , b and c? a = -1 b = 2 c = 3, so the y intercept is (0,3)**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3 axis of symmetry is x = 1 What are a , b and c? a = -1 The vertex is b = 2 c = 3**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3 Plot the points**Graph the function. Show the y intercept, axis of symmetry**and vertex f(x) = -x2 + 2x + 3 Connect the points**Homework**Page 291 # 15, 19, 23, 25, 33 – 43 odd**Homework**Page 291- 292 # 16, 22, 26, 32 - 42 even, 46, 47